Symmetry-based constant-time homonuclear dipolar recoupling in solid state NMR

Constant-time dipolar recoupling pulse sequences are advantageous in structural studies by solid state nuclear magnetic resonance (NMR) with magic-angle spinning (MAS) because they yield experimental data that are relatively insensitive to radio-frequency pulse imperfections and nuclear spin relaxation processes. A new approach to the construction of constant-time homonuclear dipolar recoupling sequences is described, based on symmetry properties of the recoupled dipole-dipole interaction Hamiltonian under cyclic displacements in time with respect to the MAS sample rotation period. A specific symmetry-based pulse sequence called PITHIRDS-CT is introduced and demonstrated experimentally. (13)C NMR data for singly-(13)C-labeled amino acid powders and amyloid fibrils indicate the effectiveness of PITHIRDS-CT in measurements of intermolecular distances in solids. (15)N-detected and (13)C-detected measurements of intramolecular (15)N-(15)N distances in peptides with alpha-helical and beta-sheet structures indicate the utility of PITHIRDS-CT in studies of molecular conformations, especially measurements of backbone psi torsion angles in peptides containing uniformly (15)N- and (13)C-labeled amino acids.     

Estimation of carbon-carbon bond lengths and medium-range internuclear distances by solid-state nuclear magnetic resonance.

We describe magic-angle-spinning NMR methods for the accurate determination of internuclear dipole-dipole couplings between homonuclear spins-(1/2) in the solid state. The new sequences use symmetry principles to treat the effect of magic-angle sample-rotation and resonant radio frequency fields. The pulse-sequence symmetries generate selection rules which reduce the interference of undesirable interactions and improve the robustness of the pulse sequences with respect to chemical shift anisotropies. We show that the pulse sequences may be used to estimate distances between 13C spins in organic solids, including bond lengths in systems with large chemical shift anisotropies, such as conjugated systems. For bond-length measurements, the precision of the method is +/-2 pm with a systematic overestimate of the internuclear distance by 3 +/- 1 pm. The method is expected to be a useful tool for investigating structural changes in macromolecules.     

Use of Nuclear Spin Noise Spectroscopy to Monitor Slow Magnetization Buildup at Millikelvin Temperatures

At ultralow temperatures, longitudinal nuclear magnetic relaxation times become exceedingly long and spectral lines are very broad. These facts pose particular challenges for the measurement of NMR spectra and spin relaxation phenomena. Nuclear spin noise spectroscopy is used to monitor proton spin polarization buildup to thermal equilibrium of a mixture of glycerol, water, and copper oxide nanoparticles at 17.5 mK in a static magnetic field of 2.5 T. Relaxation times determined in such a way are essentially free from perturbations caused by excitation radiofrequency pulses, radiation damping, and insufficient excitation bandwidth. The experimental spin‐lattice relaxation times determined on resonance by saturation recovery with spin noise detection are consistently longer than those determined by using pulse excitation. These longer values are in better accordance with the expected field dependence trend than those obtained by on‐resonance experiments with pulsed excitation.     

A contribution to the theory of multiple-pulse narrowing of NQR lines

A theory of the high resolution NQR spectroscopy experiments is developed in the framework of an average Hamiltonian approach analogous to that used in the theory of the NMR line pulse narrowing in solids. A specially constructed unitary operator is found making it possible to treat r. f. excitation of spin systems with nonequidistant spectra, spin and EFG asymmetry parameter being arbitrary. Time averaging is used to get an average Hamiltonian appropriate to dealing with arbitrary periodic multiple-pulse sequences. Relations between the sequence parameters are found ensuring realization of the averaging above mentioned in different cases of interest. The theoretical results obtained are consistent with available data on NQR multiple-pulse experiments.     

Multiple quantum NMR excitation with a one-quantum hamiltonian

Excitation of multiple quantum coherence in dipolar coupled spin systems is usually accomplished with a two-quantum multiple pulse sequence which can be time reversed by means of a 90° phase shift. The application of such an excitation scheme to a spin system in thermal equilibrium excites only even orders of multiple quantum coherence. We demonstrate here time reversible pulse sequences that excite all orders of coherence by creating a pure one-quantum average hamiltonian. We also describe pulse schemes which can be used to create pure one- or two-quantum average hamiltonians with variable scaling between +1 and −1. These excitation schemes are relevant to the study of spin clustering by multiple quantum NMR.     

臭氧分子在激光场中的多光子激发

采用二次量子化方法和酉变换讨论了O3分子在激光场中的多光子激发.推导出了O3分子的振动Hamiltonian 算子、从基态到各激发态的跃迁几率公式,以及O3分子从激光场中吸收的光子数公式,并分析了计算结果.这包括对O3分子伸缩振动能谱的计算及与实验结果的比较,跃迁几率随外场频率的变化、随时间的变化,以及O3分子在辐射场中的能量吸收情况(取光场强度为5×10-2 W/cm2).建立讨论所有具有C2v对称分子从基态到第四激发态以下各态多光子激发问题的模型.     

Optimal control design of NMR and dynamic nuclear polarization experiments using monotonically convergent algorithms

Optimal control theory has recently been introduced to nuclear magnetic resonance (NMR) spectroscopy as a means to systematically design and optimize pulse sequences for liquid- and solid-state applications. This has so far primarily involved numerical optimization using gradient-based methods, which allow for the optimization of a large number of pulse sequence parameters in a concerted way to maximize the efficiency of transfer between given spin states or shape the nuclear spin Hamiltonian to a particular form, both within a given period of time. Using such tools, a variety of new pulse sequences with improved performance have been developed, and the NMR spin engineers have been challenged to consider alternative routes for analytical experiment design to meet similar performance. In addition, it has lead to increasing demands to the numerical procedures used in the optimization process in terms of computational speed and fast convergence. With the latter aspect in mind, here we introduce an alternative approach to numerical experiment design based on the Krotov formulation of optimal control theory. For practical reasons, the overall radio frequency power delivered to the sample should be minimized to facilitate experimental implementation and avoid excessive sample heating. The presented algorithm makes explicit use of this requirement and iteratively solves the stationary conditions making sure that the maximum of the objective is reached. It is shown that this method is faster per iteration and takes different paths within a control space than gradient-based methods. In the present work, the Krotov approach is demonstrated by the optimization of NMR and dynamic nuclear polarization experiments for various spin systems and using different constraints with respect to radio frequency and microwave power consumption.     

Conversion of parahydrogen induced longitudinal two-spin order to evenly distributed single spin polarisation by optimal control pulse sequences

Strongly enhanced spin polarization in the form of longitudinal spin order can be generated on target molecules by using parahydrogen in a catalyzed hydrogenation reaction. An optimal control algorithm was used to generate radiofrequency pulse sequences which convert the arising longitudinal two-spin order into single-spin Zeeman order with high efficiency and distribute it evenly between three coupled spins within the same molecule. The pulses are designed to be very robust towards variations in the B(0) and B(1) fields. Furthermore, this strategy is applied to enhance the NMR signal in an ultrafast gradient assisted single excitation two-dimensional spectroscopy experiment.     

Measuring chirality in NMR in the presence of a static electric field

The scalar Hamiltonian of nuclear spins in the presence of a static electric field supports chirality. However, the eigenvalues of the Hamiltonian are not chiral; hence, chirality is not manifested in the usual NMR experiment. In this work, we show that the magnetization response to certain radio frequency pulse sequences exhibits chirality as well as handedness.     

Spherical tensor analysis of nuclear magnetic resonance signals

In a nuclear magnetic-resonance (NMR) experiment, the spin density operator may be regarded as a superposition of irreducible spherical tensor operators. Each of these spin operators evolves during the NMR experiment and may give rise to an NMR signal at a later time. The NMR signal at the end of a pulse sequence may, therefore, be regarded as a superposition of spherical components, each derived from a different spherical tensor operator. We describe an experimental method, called spherical tensor analysis (STA), which allows the complete resolution of the NMR signal into its individual spherical components. The method is demonstrated on a powder of a (13)C-labeled amino acid, exposed to a pulse sequence generating a double-quantum effective Hamiltonian. The propagation of spin order through the space of spherical tensor operators is revealed by the STA procedure, both in static and rotating solids. Possible applications of STA to the NMR of liquids, liquid crystals, and solids are discussed.     

Broadband inversion for MAS NMR with single-sideband-selective adiabatic pulses

We explain how and under which conditions it is possible to obtain an efficient inversion of an entire sideband family of several hundred kHz using low-power, sideband-selective adiabatic pulses, and we illustrate with some experimental results how this framework opens new avenues in solid-state NMR for manipulating spin systems with wide spinning-sideband (SSB) manifolds. This is achieved through the definition of the criteria of phase and amplitude modulation for designing an adiabatic inversion pulse for rotating solids. In turn, this is based on a framework for representing the Hamiltonian of the spin system in an NMR experiment under magic angle spinning (MAS). Following earlier ideas from Caravatti et al. [J. Magn. Reson. 55, 88 (1983)], the so-called "jolting frame" is used, which is the interaction frame of the anisotropic interaction giving rise to the SSB manifold. In the jolting frame, the shift modulation affecting the nuclear spin is removed, while the Hamiltonian corresponding to the RF field is frequency modulated and acquires a spinning-sideband pattern, specific for each crystallite orientation.     

NMR R1 rho rotating-frame relaxation with weak radio frequency fields

NMR spin relaxation in the rotating frame (R(1 rho)) is one of few methods available to characterize chemical exchange kinetic processes occurring on micros-ms time scales. R(1 rho) measurements for heteronuclei in biological macromolecules generally require decoupling of (1)H scalar coupling interactions and suppression of cross-relaxation processes. Korzhnev and co-workers demonstrated that applying conventional (1)H decoupling schemes while the heteronuclei are spin-locked by a radio frequency (rf) field results in imperfect decoupling [Korzhnev, Skrynnikov, Millet, Torchia, Kay. J. Am. Chem. Soc. 2002, 124, 10743-10753]. Experimental NMR pulse sequences were presented that provide accurate measurements of R(1 rho) rate constants for radio frequency field strengths > 1000 Hz. This paper presents new two-dimensional NMR experiments that allow the use of weak rf fields, between 150 and 1000 Hz, in R(1 rho) experiments. Fourier decomposition and average Hamiltonian theory are employed to analyze the spin-lock sequence and provide a guide for the development of improved experiments. The new pulse sequences are validated using ubiquitin and basic pancreatic trypsin inhibitor (BPTI). The use of weak spin-lock fields in R(1 rho) experiments allows the study of the chemical exchange process on a wider range of time scales, bridging the gap that currently exists between Carr-Purcell-Meiboom-Gill and conventional R(1 rho) experiments. The new experiments also extend the capability of the R(1 rho) technique to study exchange processes outside the fast exchange limit.     

Theory and applications of supercycled symmetry-based recoupling sequences in solid-state nuclear magnetic resonance

We present the theoretical principles of supercycled symmetry-based recoupling sequences in solid-state magic-angle-spinning NMR. We discuss the construction procedure of the SR26 pulse sequence, which is a particularly robust sequence for double-quantum homonuclear dipole-dipole recoupling. The supercycle removes destructive higher-order average Hamiltonian terms and renders the sequence robust over long time intervals. We demonstrate applications of the SR26 sequence to double-quantum spectroscopy, homonuclear spin counting, and determination of the relative orientations of chemical shift anisotropy tensors.     

Theoretical studies of the spin Hamiltonian parameters and the local structures for M2+ (M=Co, Mn, V and Ni) ions in CsMgCl3

The spin Hamiltonian parameters (zero-field splitting D, g factors g parallel, g perpendicular and hyperfine structure constants A parallel, A perpendicular) for M2+ (M=Co, Mn, V and Ni) ions in CsMgCl3 are studied by using the perturbation formulas of the spin Hamiltonian parameters for 3dn (n=7, 5, 3, 8) ions in trigonal symmetry based on the cluster approach. In these formulas, the contributions to the spin Hamiltonian parameters from the admixture of d orbitals of the central ions with the p orbitals of the ligands and from the trigonal distortion are included and the parameters related to these effects can be obtained from the optical spectra and the local structures of the studied systems. Based on the studies, it is found that the local trigonal distortion angle beta in the M2+ impurity center is unlike that betaH (approximately 51.71 degrees) in the host CsMgCl3. The spin Hamiltonian parameters for these divalent ions in CsMgCl3 are also satisfactorily explained by using the local angle beta. The validity of the results is discussed.     

EPR Parameters of quantum mixed-spin ferric complexes with rhombic and tetragonal symmetry

Calculations are presented for the EPR g values of ferric iron in a crystal field with axial and rhombic symmetry components for a spin state which is a quantum mechanical mixture of intermediate-spin (S = 3/2) and high-spin (S = 5/2) components. The crystal field parameter μ/δ₁ is discussed as a more fundamental measure of rhombic distortion than the spin Hamiltonian ratio E/D.     

NMR measurements of diffusion in concentrated samples: avoiding problems with radiation damping

Pulsed field gradient spin echo NMR is generally the method of choice for diffusion measurements on liquid samples. With modern high field instruments, however, severe problems can arise when it is applied to samples with very high proton concentrations because of the presence of radiation damping. The problems may be greatly reduced by a suitable choice of experimental parameters, in particular the use of modified stimulated echo pulse sequences with a reduced flip angle for the first pulse.     

Solid-state (63)Cu and (65)Cu NMR spectroscopy of inorganic and organometallic copper(I) complexes

Solid-state 63Cu and 65Cu NMR experiments have been conducted on a series of inorganic and organometallic copper(I) complexes possessing a variety of spherically asymmetric two-, three-, and four-coordinate Cu coordination environments. Variations in structure and symmetry, and corresponding changes in the electric field gradient (EFG) tensors, yield 63/65Cu quadrupolar coupling constants (CQ) ranging from 22.0 to 71.0 MHz for spherically asymmetric Cu sites. These large quadrupolar interactions result in spectra featuring quadrupolar-dominated central transition patterns with breadths ranging from 760 kHz to 6.7 MHz. Accordingly, Hahn-echo and/or QCPMG pulse sequences were applied in a frequency-stepped manner to rapidly acquire high S/N powder patterns. Significant copper chemical shielding anisotropies (CSAs) are also observed in some cases, ranging from 1000 to 1500 ppm. 31P CP/MAS NMR spectra for complexes featuring 63/65Cu-31P spin pairs exhibit residual dipolar coupling and are simulated to determine both the sign of CQ and the EFG tensor orientations relative to the Cu-P bond axes. X-ray crystallographic data and theoretical (Hartree-Fock and density functional theory) calculations of 63/65Cu EFG and CS tensors are utilized to examine the relationships between NMR interaction tensor parameters, the magnitudes and orientations of the principal components, and molecular structure and symmetry.     

Quadrupolar nuclear magnetic resonance spectroscopy in solids using frequency-swept echoing pulses

The acquisition of ideal powder line shapes remains a recurring challenge in solid-state wideline nuclear magnetic resonance (NMR). Certain species, particularly quadrupolar spins in sites associated with large electric field gradients, are difficult to excite uniformly and with good efficiencies. This paper discusses some of the opportunities that arise upon departing from standard spin-echo excitation approaches and switching to echo sequences that use low-power, frequency-swept radio frequency (rf) pulses instead. The reduced powers demanded by such swept rf fields allow one to excite spins in different crystallites efficiently and with orientation-independent pulse angles, while the large bandwidths of interest that are needed by the measurement can be covered, thanks to the use of broadband frequency sweeps. The fact that the spins' evolution and ensuing dephasing starts at the beginning of such rf manipulation calls for the use of spin-echo sequences; a number of alternatives capable of providing the desired line shapes both in the frequency and in the time domains are introduced and experimentally demonstrated. Sensitivity- and lineshape-wise these experiments are competitive vis-a-vis current implementations of wideline quadrupolar NMR based on hard rf pulses; additional opportunities that may derive from these ideas are also briefly discussed.     

NMR study of tetrahydrofuran oriented in a nematic phase

The H-1 NMR spectrum of tetrahydrofuran (THF) dissolved in the nematic phase IV (Merck) has been analysed by used of a computer program which incorporates symmetry. A satisfactory fit for the spectrum could be obtained under the assumption that the spin Hamiltonian has effective C(2v)symmetry. Comparison of the empirical values of the direct dipolar couplings with the predictions of different theoretical models shows that agreement is better for free pseudorotation than for interconversion between two equivalent conformation.     

Combined ligand field and density functional theory analysis of the magnetic anisotropy in oligonuclear complexes based on Fe(III)-CN-M(II) exchange-coupled pairs

Magnetic anisotropy in cyanide-bridged single-molecule magnets (SMMs) with Fe(III)-CN-M(II) (M = Cu, Ni) exchange-coupled pairs was analyzed using a density functional theory (DFT)-based ligand field model. A pronounced magnetic anisotropy due to exchange was found for linear Fe(III)-CN-M(II) units with fourfold symmetry. This results from spin-orbit coupling of the [Fe(III)(CN)6](3-) unit and was found to be enhanced by a tetragonal field, leading to a (2)E g ground state for Fe(III). In contrast, a trigonal field (e.g., due to tau 2g Jahn-Teller angular distortions) led to a reduction of the magnetic anisotropy. A large enhancement of the anisotropy was found for the Fe(III)-CN-Ni(II) exchange pair if anisotropic exchange combined with a negative zero-field splitting energy of the S = 1 ground state of Ni(II) in tetragonally compressed octahedra, while cancellation of the two anisotropic contributions was predicted for tetragonal elongations. A recently developed DFT approach to Jahn-Teller activity in low-spin hexacyanometalates was used to address the influence of dynamic Jahn-Teller coupling on the magnetic anisotropy. Spin Hamiltonian parameters derived for linear Fe-M subunits were combined using a vector-coupling scheme to yield the spin Hamiltonian for the entire spin cluster. The magnetic properties of published oligonuclear transition-metal complexes with ferromagnetic ground states are discussed qualitatively, and predictive concepts for a systematic search of cyanide-based SMM materials are presented.